OSA's Digital Library

Journal of Lightwave Technology

Journal of Lightwave Technology


  • Vol. 28, Iss. 4 — Feb. 15, 2010
  • pp: 423–433

Approaching the Non-Linear Shannon Limit

Andrew D. Ellis, Jian Zhao, and David Cotter

Journal of Lightwave Technology, Vol. 28, Issue 4, pp. 423-433 (2010)

View Full Text Article

Acrobat PDF (807 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

  • Export Citation/Save Click for help


We review the recent progress of information theory in optical communications, and describe the current experimental results and associated advances in various individual technologies which increase the information capacity. We confirm the widely held belief that the reported capacities are approaching the fundamental limits imposed by signal-to-noise ratio and the distributed non-linearity of conventional optical fibres, resulting in the reduction in the growth rate of communication capacity. We also discuss the techniques which are promising to increase and/or approach the information capacity limit.

© 2010 IEEE

Andrew D. Ellis, Jian Zhao, and David Cotter, "Approaching the Non-Linear Shannon Limit," J. Lightwave Technol. 28, 423-433 (2010)

Sort:  Year  |  Journal  |  Reset


  1. L. Wood, D. Blankenhdn, "State of the BBS nation: Behold lowly bulletin board now encompassing the globe," Byte 15, 298-304 (1990).
  2. 10 Gb/s Ethernet Passive Optical Network http://www.ieee802.org/3/av (2009) IEEE P802.3av Task Force, downloaded.
  3. E. B. Desurvire, "Capacity demand and technology challenges for lightwave systems in the next two decades," J. Lightw. Technol. 24, 4697-4710 (2006).
  4. P. Magill, "System technologies for 100G transport networks," Proc. OFC 2009 (2009).
  5. J. M. Kahn, K.-P. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM systems," IEEE J. Sel. Topics Quantum Electron. 10, 259-272 (2004).
  6. C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J. 27, 379–423, 623-656 (1948).
  7. C. E. Shannon, W. Weaver, The Mathematical Theory of Communication (Univ. Illinois Press, 1963).
  8. R.-J. Essiambre, "Capacity limits of fiber-optic communication systems," Proc. OFC (2009) (2009).
  9. N. Kikuchi, K. Mandai, K. Sekine, S. Sasaki, "Incoherent 32-level optical multilevel signalling technoloigies," J. Lightw. Technol. 26, 150-157 (2008).
  10. J. M. Kahn, E. Ip, "Principles of digital coherent receivers for optical communications," Proc. OFC 2009 (2009) (2009).
  11. E. Ip, A. P. T. Lau, D. J. F. Barros, J. M. Khan, "Coherent detection in optical fiber systems," Opt. Exp. 16, 753-791 (2008).
  12. E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, 2002).
  13. S. Haykin, Digital Communications (Wiley, 1988).
  14. J. G. Proakis, Digital Communications (McGraw-Hill, 2000).
  15. M. Nakazawa, "Challenges to FDM-QAM coherent transmission with ultrahigh spectral efficiency," Proc. ECOC 2008 (2008).
  16. S. Y. Chung, G. D. Forney, T. J. Richardson, R. Urbanke, "On the design of low density parity check codes within 0.0045 dB of the Shannon limit," IEEE Commun. Lett. 5, 58-60 (2001).
  17. B. Zhou, L. Zhang, J. Kang, O. Huang, Y. Y. Tai, S. Lin, M. Xu, "Non-binary LDPC codes versus Reed–Solomon codes," Proc. Inf. Theory Appl. Workshop 2008 (2008) pp. 175-184.
  18. G.709: Interfaces for the Optical Transport Network (OTN) http://www.itu.int/rec/T-REC-G.709/en downloaded from.
  19. R. W. Chang, "Synthesis of band-limited orthogonal signals for multichannel data transmission," Bell Syst. Tech. J. 45, 1775-1796 (1966).
  20. R. R. Mosier, R. G. Clabaugh, "Kineplex, a bandwidth efficient binary transmission system," AIEE Trans. 76, 723-728 (1958).
  21. H. Sanjoh, E. Yamada, Y. Yoshikuni, "Optical orthogonal frequency division multiplexing using frequency/time domain filtering for high spectral efficiency up to 1 bit/s/Hz," Proc. OFC'02 (2002).
  22. A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, S. Matsuoka, R. Kudo, K. Ishihara, Y. Takatori, M. Mizoguchi, K. Okada, K. Hagimoto, H. Yamazaki, S. Kamei, H. Ishii, "13.4-Tb/s (134$\,\times\,$111-Gb/s/ch) no-guard-interval coherent OFDM transmission over 3 600 km of SMF with 19-ps average PMD," Proc. ECOC'08 (2008).
  23. K. Takiguchi, M. Oguma, T. Shibata, H. Takahashi, "Optical OFDM demultiplexer using silica PLC based optical FFT circuit," Proc. OFC 2009 (2009).
  24. A. D. Ellis, F. C. G. Gunning, "Filter strategies for coherent WDM," Proc. Emerging Technol. Opt. Sci. (2004).
  25. A. D. Ellis, F. C. G. Gunning, "Spectral density enhancement using coherent WDM," IEEE Photon. Technol. Lett. 17, 504-506 (2005).
  26. J. Zhao, A. D. Ellis, "Performance improvement using a novel MAP detector in coherent WDM systems," Proc. ECOC'08 (2008).
  27. T. Healy, F. C. G. Gunning, E. Pincemin, B. Cuenot, A. D. Ellis, "1 200 km SMF (100 km spans) 280 Gbit/s coherent WDM transmission using hybrid Raman/EDFA amplification," ECOC'07 Berlin (2007) paper Mo1.3.5.
  28. A. J. Lowery, J. Armstrong, "Orthogonal frequency division multiplexing for dispersion compensation of long-haul optical systems," Opt. Exp. 2006 14, 2079-2084 (2006).
  29. B. J. C. Schmidt, Z. Zan, L. B. Du, A. J. Lowery, "100 Gbit/s transmission using single band direct detection optical OFDM," Proc. OFC'09 (2009).
  30. I. B. Djordjevic, B. Vasic, "100-Gb/s transmission using orthogonal frequency-division multiplexing," IEEE Photon. Technol. Lett. 18, 1576-1578 (2006).
  31. S. L. Jansen, I. Morita, H. Tanaka, "10-Gb/s OFDM with conventional DFB lasers," Proc. ECOC'07 (2007).
  32. W. Shieh, "High spectral efficiency coherent optical OFDM for 1 Tb/s ethernet transport," Proc. OFC 2009 (2009).
  33. S. L. Jansen, I. Morita, N. Takeda, H. Tanaka, "20-Gb/s OFDM transmission over 4 160-km SSMF enabled by RF-pilot tone phase noise compensation," Proc. OFC Conf. 2007 (2007).
  34. H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, H. Tanaka, "DWDM transmission with 7.0 bit/s/Hz spectral efficiency using 8$\,\times\,$65.1 Gbit/s coherent PDM OFDM signals," Proc. OFC 2009 (2009).
  35. X. Yi, W. Shieh, Y. Ma, "Phase noise on coherent optical OFDM systems with 16-QAM and 64-QAM beyond 10 Gb/s," Proc. ECOC'07 (2007).
  36. T. Miki, H. Ishio, "Viabilities of the wavelength-division-multiplexing transmission system over an optical fiber cable," IEEE Trans. Commun. 26, 1082-1087 (1978).
  37. A. D. Ellis, F. C. G. Gunning, B. Cuenot, T. C. Healy, E. Pincemin, M. Rukosueva, "Towards 1TbE using coherent WDM," Proc. OECC/ACOFT 2008 (2008).
  38. F. C. G. Gunning, T. Healy, X. Yang, A. D. Ellis, "0.6 Tbit/s capacity and 2 bit/s/Hz spectral efficiency at 42.6 Gsymbol/s using a single DFB laser with NRZ coherent WDM and polarisation multiplexing," Proc. CLEO Eur. 2007 (2007).
  39. Y. Ma, Q. Yang, Y. Tang, S. Chen, W. Shieh, "1 Tb/s per channel coherent optical OFDM transmission with subwavelength bandwidth access," Proc. OFC'09 (2009).
  40. J. Armstrong, "Peak-to-average power reduction for OFDM by repeated clipping and frequency domain filtering," Electron. Lett. 38, 246-248 (2002).
  41. D. J. Malyon, T. Widdowson, E. G. Bryant, S. F. Carter, J. V. Wright, W. A. Stallard, "Demonstration of optical pulse propagation over 10000 km of fibre using recirculating loop," Electron. Lett. 27, 120-121 (1991).
  42. H. J. Thiele, R. I. Killey, P. Bayvel, "Influence of fibre dispersion and bit rate on cross-phase-modulation-induced distortion in amplified optical fibre links," Electron. Lett. 34, 2050-2051 (1998).
  43. A. D. Ellis, W. A. Stallard, "Four wave mixing in ultra long transmission systems incorporating linear amplifiers," IEE Colloquium, No. 159 (1990).
  44. R.-J. Essiambre, B. Mikkelsen, G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576-1578 (1999).
  45. A. D. Ellis, J. D. Cox, D. Bird, J. Regnault, J. V. Wright, W. A. Stallard, "5 Gbit/s soliton propagation over 350 km with large periodic dispersion coefficient perturbations using erbium doped fibre amplifier repeaters," Electron. Lett. 27, 878- (1991).
  46. I. Morita, K. Tanaka, N. Edagawa, M. Suzuki, "Impact of the dispersion map on long-haul 40 Gbith single-channel soliton transmission with periodic dispersion compensation," Proc. OFC'99 (1999).
  47. P. V. Mamyshev, L. F. Mollenauer, "Pseudo-phase-matched four-wave mixing in soliton wavelength-division multiplexing transmission," Opt. Lett. 21, 396-398 (1996).
  48. N. J. Smith, N. J. Doran, "Modulational instabilities in fibers with periodic dispersion management," Opt. Lett. 21, 570-572 (1996).
  49. E. Pincemin, A. Tan, A. Bezard, A. Tonello, S. Wabnitz, J.-D. Ania-Castañòn, S. Turitsyn, "Robustness of 40 Gb/s ASK modulation formats in the practical system infrastructure," Opt. Exp. 14, 12049-12062 (2006).
  50. P. P. Mitra, J. B. Stark, "Nonlinear limits to the information capacity of optical fibre communications," Nature 411, 1027-1030 (2001).
  51. L. G. L. Wegener, B. M. L. Povinelli, A. G. Green, P. P. Mitra, J. B. Stark, P. B. Littlewood, "The effect of propagation nonlinearities on the information capacity of WDM optical fiber systems: Cross-phase modulation and four-wave mixing," Physica D: Nonlinear Phenomena 189, 81-99 (2004).
  52. R. J. Essiambre, G. J. Foschini, P. J. Winzer, G. Kramer, "Exploring capacity limits of fibre-optic mommunication systems," Proc. ECOC 2008 (2008).
  53. A. D. Ellis, S. J. Pycock, D. A. Cleland, C. H. F. Sturrock, "Dispersion compensation in a 450 km transmission system employing standard fibre," Electron. Lett. 28, 954 (1992).
  54. D. McGhan, C. Laperle, A. Savehenko, L. Chuandong, G. Mak, M. O'Sullivan, "5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation," Proc. OFC 2005 (2005).
  55. J. H. Winters, R. D. Gitlin, "Electronic signal processing techniques in long haul fiber optic systems," IEEE Trans. Commun. 38, 1439-1453 (1990).
  56. M. E. McCarthy, J. Zhao, A. D. Ellis, P. Gunning, "Full-field electronic dispersion compensation of 10 Gbit/s OOK without Raman amplification over 4$\,\times\,$124 km field-installed SSF," J. Lightw. Technol. 27, 5327-5335 (2009).
  57. M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photon. Technol. Lett. 16, 674-676 (2004).
  58. X. Liu, X. Wei, R. E. Slusher, C. J. McKinstrie, "Improving transmission performance in differnetioal phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27, 1616-1618 (2002).
  59. K. Kikuchi, "Electronic post-compensation for nonlinear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver," Opt. Exp. 16, 889-896 (2008).
  60. L. F. Mollenauer, A. Grant, X. Liu, X. Wei, C. Xie, I. Kang, C. Doerr, "Demonstration of 109$\,\times\,$10 G dense WDM over more than 18 000 km using novel, periodic-group-delay complemented dispersion compensation and dispersion managed solitons," Proc. ECOC 03 (2003).
  61. C. Xu, X. Liu, X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Topics Quantum Electron. 10, 281-293 (2004).
  62. W. Pieper, C. Kurtze, R. Schnabel, D. Bruer, R. Ludwig, K. Petermann, "Nonlinearity insensitive standard fibre transmission based on optical phase conjugation in a semiconductor amplifier," Electron. Lett. 30, 724-725 (1992).
  63. S. Watanabe, M. Shirasaki, "Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation," J. Lightw. Technol. 14, 243-248 (1996).
  64. K. Roberts, C. Li, L. Strawczynski, M. O'Sullivan, I. Hardcastle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18, 403-405 (2006).
  65. J. B. Stark, P. P. Mitra, A. Sengupta, "Information capacity for optical communication channels," Opt. Fiber Technol. 7, 275- (2001).
  66. B. Wu, E. Narimanov, "Information capacity of nonlinear fiber-optical systems," Proc. 2005 Quantum Electron. Laser Sci. Conf. (QELS) (2005).
  67. A. Mecozzi, M. Shtaif, "On the capacity of intensity modulated systems using optical amplifiers," IEEE Photon. Technol. Lett. 13, 1029-1031 (2001).
  68. R.-J. Essiambre, G. J. Foschini, P. J. Winzer, G. Kramer, E. C. Burrows, "The capacity of fiber-optic communication systems," Proc. OFC2008 (2008).
  69. H. Goto, M. Yoshida, T. Omiya, K. Kasai, M. Nakazawa, "Polarisation and frequency division multiplexed 1G symbol/s, 64 QAM coherent optical transmission with 8.6 b/s/Hz spectral efficiency over 160 km," IEICE Electron. Exp. 5, 776-781 (2008).
  70. S. L. Jansen, D. van den Borne, C. Climent, M. Serbay, C.-J. Weiske, H. Suche, P. M. Krummrich, S. Spalter, S. Calabro, N. Hecker-Denschlag, P. Leisching, W. Rosenkranz, W. Sohler, G. D. Khoe, T. Koonen, H. de Waardt, "10 200 km 22$\,\times\,$2$\,\times\,$l0 Gbit/s RZ-DQPSK dense WDM transmission without inline dispersion compensation through optical phase conjugation," Proc. OFC'05 (2005).
  71. L. Becouarn, G. Vareille, P. Pecci, J. F. Marcerou, "3 Tbit/s transmission (301 DPSK channels at 10.709 Gb/s) over 10270 km with a record efficiency of 0.65(bit/s)/Hz," Proc. ECOC 03 (2003).
  72. Y. Kodama, S. Wabnitz, "Reduction of soliton interaction forces by bandwidth limited amplification," Electron. Lett. 27, 1931-1932 (1991).
  73. J. Zhao, A. D. Ellis, F. C. G. Gunning, P. Frascella, S. K. Ibrahim, R. Weerasuriya, "High-capacity transmission using coherent WDM (invited)," OECC 2009 Hong Kong (2009).
  74. M. Seimetz, L. Molle, D.-D. Gross, B. Auth, R. Freund, "Coherent RZ-8 PSK transmission at 30 Gbit/s over 1200 km employing homodyne detection with digital carrier phase estimation," Proc. ECOC'07 (2007).
  75. A. H. Gnauck, G. Charlet, P. Tran, P. Winzer, C. Doerr, J. Centanni, E. Burrows, T. Kawanishi, T. Sakamoto, K. Higuma, "25.6-Tb/s C+L-band transmission of polarization-multiplexed RZ-DQPSK signals," Proc. OFC 2007 (2007).
  76. M. Yoshida, H. Goto, K. Kasai, M. Nakazawa, "64 and 128 coherent QAM optical transmission over 150 km using frequency-stabilized laser and heterodyne PLL detection," Opt. Exp. 16, 829-840 (2008).
  77. I. Morita, N. Edagawa, "50 GHz-spaced 64$\,\times\,$42.7 Gbit/s transmission over 8200 km using pre-filtered CS-RZ DPSK signal and EDFA Repeaters," Proc. ECOC'03 (2003).
  78. A. J. Lowery, "Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM," Opt. Exp. 15, 12965- (2007).
  79. E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, M. Koga, "Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system," IEEE Photon. Technol. Lett. 19, 9-11 (2007).
  80. L. Thylen, E. Berglind, O. Nilsson, "Channel capacity of optical fibres," Private Communication (2002).
  81. H. A. Haus, Y. Yamamoto, "Quantum circuit theory of phase sensitive linear systems," IEEE J. Quantum Electron. QE-23, 212-221 (1987).
  82. S. Oda, H. Sunnerud, P. A. Andrekson, "High efficiency and high output power fiber-optic parametric amplifier," Opt. Lett. 32, 1776-1778 (2007).
  83. J. M. C. Boggio, C. Lundström, J. Yang, H. Sunnerud, P. A. Andrekson, "Double-pumped FOPA with 40 dB flat gain over 81 nm bandwidth," Proc. ECOC 2008 (2008).
  84. G. Charlet, M. Salsi, H. Mardoyan, P. Tran, J. Renaudier, S. Bigo, M. Astruc, P. Sillard, L. Provost, F. Cérou, "Transmission of 81 channels at 40 Gbit/s over a transpacific-distance erbium-only link, using PDM-BPSK modulation, coherent detection, and a new large effective area fibre," Proc. ECOC'08 (2008).
  85. P. J. Roberts, F. Couny, H. Sabert, B. Mangan, D. Williams, L. Farr, M. Mason, A. Tomlinson, T. Birks, J. Knight, P. St. J. Russell, "Ultimate low loss of hollow-core photonic crystal fibres," Opt. Exp. 13, 236-244 (2005).
  86. K. Tajima, J. Zhou, K. Nakajima, K. Kurokawa, "Ultra low loss and long length photonic crystal fiber," Proc. OFC'04 (2004).
  87. R. M. Percival, D. Szebesta, C. P. Seltzer, S. D. Perin, S. T. Devey, M. Louka, "A 1.6- $\mu$m pumped 1.9- $\mu$m thulium-doped fluoride fiber laser and amplifier of very high efficiency," IEEE J. Quantum Electron. 31, 489-493 (1995).
  88. A. Krier, Y. Mao, "High performance uncooled InAsSbP/InGaAs photodiodes for the 1.8–3.4 $\mu$m wavelength range," Infrared Phys. Technol. 38, 397-403 (1997).
  89. Z. Tong, Q. Yang, Y. Ma, W. Shieh, "21.4 Gb/s coherent optical OFDM transmission over 200 km multimode fiber," Proc. OECC/ACOFT 2008 (2008).
  90. M. Bigot-Astruc, F. Gooijer, N. Montaigne, P. Sillard, "Trench-assisted profiles for large-effective-area single-mode fibers," Proc. ECOC'08 (2008).
  91. C. Rasmussen, T. Fjelde, J. Bennike, L. Fenghai, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, P. Reeves-Hall, "DWDM 40 G transmission over trans-pacific distance (10 000 km) using CSRZ-DPSK, enhanced FEC, and all-Raman-amplified 100-km ultrawave fiber spans," J. Lightw. Technol. 21, 203-207 (2004).
  92. S. Ten, "Advanced fibers for submarine and long-haul applications," Proc. LEOS 2004 pp. 543-544.
  93. C. K. Ramaiah, "Bulletin board systems for libraries," DESIDOC Bull. Inf. Technol. 15, 23-31 (1995).

Cited By

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited